I bought a triplex at the end of April this year, inheriting all three occupied units, so far so good.

Hey Kevin,Yes, 2 units have long term lease at $2,500 and $2,800 , 1 is Airbnb with $5-8k, 1 unit was occupied by owner but will be listed at $3000 this month 

Hi guys, is it possible to refinance my personal residence and immediately go buy another house as owner occupied ?

After months of searching for properties I've identified a multi-family that perfectly fits my criteria but due to life events (getting married and my future wife and I bought a primary residence) I'm short of the typical 20% down payment that most lenders are requiring since I will not be occupying the property.

I believe you are in luck as I believe there is a exclusion for owner occupied duplex.  

FHA is Owner occupied

Is there an order to start with to avoid disqualifying for another one after occupying the 1st, then 2nd for the required year terms?

Here is the scenario: 7-unit tenant-occupied property purchased a week ago from a wholesaler.

I know FHA has a few requirements regarding having multiple owner occupied loans at once. 

I need to vacate front unit tenants so that I may occupy the property.